Question

Please explain this to me!

Answer 1

One meaning of a 'linear' equation is that if you draw the graph
of the equation, the graph will be a straight line.

That's an easy way to test the equation . . . find 3 points on the
graph, and see whether they're all in a straight line.

This equation is        y  =  4 / x .

To find a point on the graph, just pick any number for 'x',
and figure out the value of 'y' that goes with it.
Do that 3 times, and you've got 3 points on the graph.

Here ... I'll do 3 quick points:

Point-A:  x = 1     y =  4 / 1    =  4
Point-B:  x = 2     y =  4 / 2    =  2
Point-C:  x = 4     y =  4 / 4    =  1

Look at this:

Slope of the line from point-A to point-B
                         = (change in 'y') / (change in 'x') =  -2 .

Slope of the line from point-B to point-C
                         = (change in 'y') / (change in 'x') =  -1/2 .

The two pieces of line from A-B and from B-C don't even have
the same slope, so they're not pieces of the same straight line !
So my points A, B, and C are NOT in a straight line.

So the equation is NOT linear.

Try it again with three points of your own.